How to sketch y=(-3x^2 +1)/(x^2)

Thread starter TyErd
Start date Feb 10, 2010
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In summary, the equation y=(-3x^2 +1)/(x^2) is a rational function with a numerator of -3x^2+1 and a denominator of x^2. To sketch the graph, a table of values can be created and the properties of the function can be used to help. The x-intercept can be found by setting y=0, but there is no y-intercept as the function is undefined at x=0. There are two asymptotes for the function, a horizontal asymptote at y=-3 and a vertical asymptote at x=0. As x approaches infinity or negative infinity, the function approaches the horizontal asymptote at y=-3.

Feb 10, 2010

TyErd

How to sketch y=(-3x^2 +1)/(x^2)

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Feb 10, 2010

Mentallic

Homework Helper

Similar deal to your hyperbola question you made previously.

[tex]\frac{-3x^2+1}{x^2}=\frac{-3x^2}{x^2}+\frac{1}{x^2}=-3+\frac{1}{x^2}[/tex]

so now you should be able to sketch the graph using already known graphs such as [itex]y=\frac{1}{x^2}[/itex]

Related to How to sketch y=(-3x^2 +1)/(x^2)

What is the equation y=(-3x^2 +1)/(x^2)?

This equation is a rational function, where the output (y) is determined by plugging in a value for x. The function is a fraction, with the numerator being -3x^2+1 and the denominator being x^2.

How do I sketch the graph of y=(-3x^2 +1)/(x^2)?

To sketch the graph, you can start by creating a table of values. Choose a few values for x and plug them into the equation to find the corresponding values for y. Plot these points on a graph and connect them with a smooth curve. Additionally, you can use the properties of the function (such as the intercepts, asymptotes, and end behavior) to help with the sketch.

What are the intercepts of y=(-3x^2 +1)/(x^2)?

To find the x-intercept, set y=0 and solve for x. In this case, it is not possible to have a y-intercept since the function is undefined at x=0 (since we cannot divide by 0).

Are there any asymptotes for y=(-3x^2 +1)/(x^2)?

Yes, there are two asymptotes for this function. As x approaches infinity or negative infinity, the function approaches a horizontal asymptote at y=-3. Additionally, there is a vertical asymptote at x=0, since the denominator becomes 0 at this point.

What is the end behavior of y=(-3x^2 +1)/(x^2)?

As x approaches infinity or negative infinity, the function approaches a horizontal asymptote at y=-3. This means that the graph will get closer and closer to the line y=-3, but it will never touch it.